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Choice probability generating functions

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  • Fosgerau, Mogens
  • McFadden, Daniel
  • Bierlaire, Michel

Abstract

This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications. The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended to competing risk survival models.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 24214.

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Date of creation: 2010
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Handle: RePEc:pra:mprapa:24214

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Keywords: Discrete choice; random utility; mixture models; duration models; logit; generalised extreme value; multivariate extreme value;

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  1. de Palma, Andre & Kilani, Karim, 2007. "Invariance of conditional maximum utility," Journal of Economic Theory, Elsevier, vol. 132(1), pages 137-146, January.
  2. P O Lindberg & E A Eriksson & L-G Mattsson, 1995. "Invariance of achieved utility in random utility models," Environment and Planning A, Pion Ltd, London, vol. 27(1), pages 121-142, January.
  3. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
  4. McFadden, Daniel, 1974. "The measurement of urban travel demand," Journal of Public Economics, Elsevier, vol. 3(4), pages 303-328, November.
  5. Ruud H Koning & Geert Ridder, 1999. "Discrete Choice and Stochastic Utility Maximization," Economics Working Paper Archive 413, The Johns Hopkins University,Department of Economics.
  6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, September.
  7. Bierlaire, M. & Bolduc, D. & McFadden, D., 2008. "The estimation of generalized extreme value models from choice-based samples," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 381-394, May.
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Cited by:
  1. Fosgerau, Mogens & Frejinger, Emma & Karlström, Anders, 2013. "A link based network route choice model with unrestricted choice set," Working papers in Transport Economics 2013:10, CTS - Centre for Transport Studies Stockholm (KTH and VTI).
  2. Daniel L. McFadden & Mogens Fosgerau, 2012. "A theory of the perturbed consumer with general budgets," NBER Working Papers 17953, National Bureau of Economic Research, Inc.
  3. Pereira, Pedro & Ribeiro, Tiago & Vareda, João, 2013. "Delineating markets for bundles with consumer level data: The case of triple-play," International Journal of Industrial Organization, Elsevier, vol. 31(6), pages 760-773.
  4. Joao Macieira & Pedro Pereira & Joao Vareda, 2013. "Bundling Incentives in Markets with Product Complementarities: The Case of Triple-Play," Working Papers 13-15, NET Institute.

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